A robust estimation based on penalised regularisation for the varying-coefficient additive model

To effectively handle functional data and longitudinal data, we propose a robust estimation approach based on penalised regularisation with the framework of the varying-coefficient additive model. Our method utilises an iterative backfitting algorithm that leverages splines to estimate the component functions. The proposed algorithm showcases both stability and effectiveness in model fitting, particularly when dealing with scenarios involving high-dimensional covariates and high levels of noise. We establish a comprehensive theoretical framework for the proposed method. Furthermore, we investigate the asymptotic normality of the estimators and construct asymptotic confidence bands to quantify the uncertainty of the estimates. To validate the performance of our method, we conduct extensive simulation studies and compare the results with those obtained using alternative approaches. Additionally, we apply our proposed method to a real dataset focussed on young high school dropouts in the US, demonstrating its practical applicability.